Construction of Three-Qubit Kochen-Specker Sets

S.P. Toh Faculty of Engineering, The University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan, Malaysia

Received: January 20, 2015; In final form: February 24, 2016

Full Text PDF

Contextuality is one of the fundamental deviations of quantum mechanics from classical physics. The Kochen-Specker theorem shows that non-contextual classical physics with hidden variables is inconsistent with the predictions of quantum mechanics. Parity proof is one of the many different approaches applied to prove Kochen-Specker theorem for quantum system with different dimensionality. This method of proof requires Kochen-Specker sets that were composed of an odd number of bases and an even number of projectors. In most of the cases, the number of Kochen-Specker sets produced is large and its production is generally aided by computer calculation. However, manual generation of the Kochen-Specker sets are also reported previously for qutrit and two-qubit systems. We put forward the first and surprisingly simple method to generate manually Kochen-Specker sets, with respect to the Mermin pentagram, that can be used for the parity proof of the Kochen-Specker theorem in a state space of eight-dimensional three-qubit system.

DOI: 10.12693/APhysPolA.129.273 PACS numbers: 03.65.Aa, 03.65.Ta, 42.50.Dv